The purpose of this paper is to analyze the free vibration behavior of functionally graded Timoshenko beams with simply-supported (S-S), clamped-clamped (C-C) and clamped-free (C-F) boundary conditions using the coupled displacement field (CDF) method.
Based on the power law exponent form, material properties of the beam continuously differ in the direction of thickness. The approach uses the CDF method, where the admissible trial functions are assumed for total rotation, which satisfies various boundary conditions. By using coupling equations, the function for the lateral displacement field is derived in terms of the total rotations. The undetermined coefficients are derived by using the energy formulations. By minimizing the Lagrangian with respect to the undetermined coefficients, the frequency parameters are obtained.
The frequencies with respect to different parameters such as slenderness ratios (l/h) and power law (k) for all edges S-S, C-C and C-F boundary conditions are found. The effect of the parameters on the acquired frequencies is noticed, which was compared with different methods in the literature to verify the derived frequencies, which are found to be in excellent accord.
When compared to the Rayleigh–Ritz method, the energy formulations in the proposed CDF method comprise half the number of undetermined coefficients, which significantly reduces the vibration problem. The efficiency of the suggested approach in determining the frequency parameters is found in its shorter computational process in contrast to other methods.
